A Note on Local Mode-in-State Participation Factors for Nonlinear Systems
For researchers in nonlinear systems analysis, this provides a theoretical extension of a known method, but the contribution is incremental as it directly adapts existing linear techniques.
This paper extends a probabilistic approach to modal participation factors from linear to smooth nonlinear autonomous systems, deriving explicit formulas under symmetry assumptions on initial state uncertainty.
The paper studies an extension to nonlinear systems of a recently proposed approach to the concept of modal participation factors. First, a definition is given for local mode-in-state participation factors for smooth nonlinear autonomous systems. The definition is general, and, unlike in the more traditional approach, the resulting participation measures depend on the assumed uncertainty law governing the system initial condition. The work follows Hashlamoun, Hassouneh and Abed (2009) in taking a mathematical expectation (or set-theoretic average) of a modal contribution measure with respect to an assumed uncertain initial state. As in the linear case, it is found that a symmetry assumption on the distribution of the initial state results in a tractable calculation and an explicit and simple formula for mode-in-state participation factors.